I think having something like that would be really cool and very convenient. One wouldn't need to worry about downloading a separate bitcoin client, but could simply load up the application in the browser and be good to go.

New P2P and real time communications APIs currently under development by W3C could revolutionize the architecture of the web and the way users can interact with one another.Currently the web is mostly a client-server architecture. That is the web browser connects to a server to download a page or any data for that matter. Servers are the single source of information on the web and browsers are their clients. This could be all about to change and so bring about the biggest revolution since the web was invented. If you think HTML5 or Ajax are important, then the new P2P and real time communications APIs that are under development by W3C should open your eyes to the fact that it is a much bigger world out there than you have so far dreamed of.